The presumptive presidential nominees — Democrat Hillary Clinton and Republican Donald Trump —gave dueling speeches on June 13 in the aftermath of the Orlando mass shooting. We combed through the speeches to find factual assertions that were worthy of fact checking. There were many more such claims, of dubious provenance, in Trump’s speech, so his section of the fact check is longer.

The quotes are in the order in which they were delivered. As is our custom in such roundups, we do not provide a Pinocchio rating.

Hillary Clinton

“If you’re too dangerous to get on a plane, you are too dangerous to buy a gun in America.”

There’s renewed push among gun-control advocates to ban known or suspected terrorists from buying guns. This phrase has been used to explain provisions in the February 2015 amendment introduced by Sen. Dianne Feinstein (D-Calif.) in the Senate, and Rep. Peter King (R-N.Y.) in the House. Clinton has repeated it on the trail since the San Bernardino, Calif., shooting.

We’ve explored this rhetoric in the past and found it misleading when referring to the proposal that Feinstein introduced. The “no fly” list is a database that the Transportation Security Administration uses to screen passengers, and people on the list are deemed a threat to commercial aviation or national security. This list is a subset of a larger watch list, the FBI’s Terrorist Screening Center’s consolidated Terrorist Watchlist. The Feinstein amendment applied to the people in the larger consolidated list, not directly tied to the no-fly list.

The government uses a “reasonable suspicion” standard to nominate and include someone in the Terrorist Watchlist. Belonging to a terrorist organization, or being listed on one of the watch lists, does not automatically stop someone from buying a gun. If a person on a watch list tries to buy a gun, the FBI is notified. There has to be another factor that disqualifies the person from buying a gun under federal or state law, such as a felony conviction or illegal immigration status.

According to FBI Director James Comey, the gunman in the Orlando shooting was once on a terrorism watch list. But he was taken off the list after FBI officials did not find enough evidence to charge him. It’s unclear how the proposal that Clinton has supported would have intervened in this case.

“I know some will say that assault weapons and background checks are totally separate issues having nothing to do with terrorism. Well, in Orlando and San Bernardino terrorists used assault weapons, the AR-15. And they used it to kill Americans. That was the same assault weapon used to kill those little children in Sandy Hook.”

Many of our readers have inquired about the difference between “assault weapon” and “assault rifle,” given media reports using the terms interchangeably. This line by Clinton refers to the weapon used in Orlando and San Bernardino: the AR-15.

[Update, June 14: New reports say that the Orlando shooter used a .223 AR-style Sig Sauer MCX semiautomatic rifle and a Glock 17 9 mm handgun. The Sig Sauer could be considered an AR-style weapon but it is a little different from the AR-15.]

Clinton has called for a new ban on assault weapons, after the previous assault-weapons ban expired in 2004 after 10 years. There is mixed evidence as to how effective that ban was, and dispute over the efficacy of bans on certain weapons and large-capacity magazines in general. (Related: See our fact-check on whether proposed gun-control laws since the Newtown shooting in 2012 would have affected those shootings.)

Our colleague Thomas Gibbons-Neff on “Checkpoint” has a helpful explanation of the history of the AR-15. The AR-15 is the civilian version of the M-16, the Army’s standard-issue rifle. It’s commonly referred to as an “assault rifle,” but that term doesn’t apply to all AR-15s since not all are fully automatic.

As Gibbons-Neff explained: Known to the masses as an “AR-15 assault rifle” and frequently misnamed as a “machine gun,” the AR-15 is sold mostly as a semiautomatic weapon only, meaning one pull of the trigger equates to one bullet leaving the barrel. An assault rifle, by definition, means that the weapon is fully automatic.

Fully automatic AR-15s are available in the United States, but they require extensive paperwork from the bureau of Alcohol, Tobacco and Firearms and are exponentially more expensive than their single-fire counterparts. That being said, certain modifications to the weapon’s trigger assembly can enable some semiautomatic AR-15s for fully automatic fire.

“For starters, it is long past time for the Saudis, the Qataris and the Kuwaitis and others to stop their citizens from funding extremist organizations.”

This has long been an issue for the U.S. government, which has jawboned these countries to little effect. A 2009 State Department cable, issued when Clinton was secretary of state and later released by WikiLeaks, detailed the talking points that were to be delivered to officials in Saudi Arabia, Qatar and Kuwait, urging yet again that action be taken to stem the financing of terrorist groups through private donations. In recent years, government officials say, the Saudis and Qataris have cracked down but Kuwait remains a problem.

We should also note that such concerns did not prevent the Clinton Foundation from accepting millions of dollars from these countries — $10 million to $25 million from Saudi Arabia, $5 million to $10 million from Kuwait and $1 million to $5 million from Qatar.

“It’s no coincidence that hate crimes against American Muslims and mosques have tripled after Paris and San Bernardino.”

Clinton suggests this is a current statistic, but it is based on just one month of data after the Paris and San Bernardino attacks, collected by the Center for the Study of Hate and Extremism at California State University. Brian Levin, the center’s director, told The Fact Checker that the center did not collect data after Jan. 1, and he acknowledged that it represents a “small data set.” But he noted that it reflected a trend of anti-Muslim actions that have spiked after previous instances, mostly notably after the Sept. 11, 2001, attacks.

Donald Trump

“Even her former Secret Service agent, who’s seen her under pressure and in times of stress, has stated that she lacks the temperament and integrity to be our president.”

“The killer, whose name I will not use, or ever say, was born in Afghan, of Afghan parents, who immigrated to the United States.”

Twitter commentary quickly noted that Trump was wrong, that the shooter was born in the United States. But Trump, using a teleprompter, misspoke. His prepared text correctly stated that Omar Mateen was born an American citizen.

“Even our own FBI director has admitted that we cannot effectively check the backgrounds of people we’re letting into America.”

Trump overstated what FBI Director James Comey said in congressional testimony.

Comey made his remarks in response to a bill that would have required the FBI chief to personally certify that every single refugee admitted into the country was not a security threat. “Could I certify to there being no risk associated with an individual?” Comey said on Dec. 9. “The bureau doesn’t take positions on legislation, and we don’t get involved in policy decisions. But that practically would be impossible.”

Comey has made it clear that the process in place to vet refugees has gotten better but there is nothing that is “risk-free.”

“All of the September 11th hijackers were issued visas. Large numbers of Somali refugees in Minnesota have tried to join ISIS.”

Trump is correct that the 19 hijackers in the 9/11 attacks had visas — though some of them had overstayed their visas. Five other co-conspirators applied for visas, but were denied. Two others also obtained visas, but were not a part of the actual attacks, according to the 9/11 Commission staff report.

There is a concentration of ethnic Somalis in Minneapolis who have joined known terrorist groups, such as al-Shabab and the Islamic State, or ISIS. But the numbers are not large. According to George Washington University’s report on U.S.-grown extremism, at least 15 individuals since 2014 have traveled or tried to travel from the United States to join ISIS, relying “on a well-worn recruiting apparatus that leveraged deep personal, familial and community relations.” Minnesota had the second-highest number of arrests (11) made in a state connected to ISIS-related activities in 2015 alone, behind New York.

“Immigration from Afghanistan into the United States has increased nearly fivefold — fivefold — in just one year. According to Pew Research, 99 percent of the people in Afghanistan support oppressive sharia law.”

Trump may be referring to the increase in grants of legal permanent residence to Afghans from fiscal 2013 (2,196) to fiscal 2014 (10,527). The increase resulted from additional visas granted through the Special Immigrant Visa Program for Afghans who were interpreters for the military or worked for the U.S. government, according to the Migration Policy Institute. Congress allowed this fix due to backlogs in processing the cases.

Trump cites Pew’s research that 99 percent of Muslims in Afghanistan support sharia law as the official law. But Pew also notes that nearly 30 percent of Muslims in Afghanistan “say sharia should be open to multiple interpretations,” and that people often disagree on what “sharia law” means.

“Here is what she [Clinton] said, exact quote, ‘Muslims are peaceful and tolerant people, and have nothing whatsoever to do with terrorism.’ That is Hillary Clinton.”

He is referring to this tweet, which prefaced the comment with the observation that “Islam is not our adversary:”

"Let’s be clear: Islam is not our adversary. Muslims are peaceful and tolerant people and have nothing whatsoever to do with terrorism."

“Her plan is to disarm law-abiding Americans, abolishing the Second Amendment, and leaving only the bad guys and terrorists with guns…. She wants to take away Americans’ guns and then admit the very people who want to slaughter us.”

Nope, Clinton does not want to abolish the Second Amendment.

Our friends at FactCheck.org and PolitiFact both debunked this. Clinton has consistently said she supported protecting Americans’ constitutional right to bear arms. Her gun violence prevention proposal includes plans to make certain gun purchases a federal crime, and ban certain type of guns (assault weapons).

Let’s not forget that Trump himself used to support an assault weapons ban, as he wrote in his 2000 book, “The America We Deserve”: “I generally oppose gun control, but I support the ban on assault weapons and I support a slightly longer waiting period to purchase a gun.”

“Hillary Clinton’s catastrophic immigration plan will bring vastly more radical Islamic immigration into this country, threatening not only our society but our entire way of life.… The burden is on Hillary Clinton to tell us how she will pay for it; her plan will cost hundreds of billions of dollars long term.”

We can’t fact-check whether Clinton’s plan is “catastrophic;” we’ll let readers judge that for themselves. It’s unclear where Trump is getting the cost estimate on the “hundreds of billions of dollars,” but it seems wildly exaggerated. The Committee for a Responsible Federal Budget found that the immigration reform component of Clinton’s plan would save the federal budget $100 billion over 10 years.

“Each year the United States permanently admits 100,000 immigrants from the Middle East and many more from Muslim countries outside of the Middle East.”

You get to around 100,000 only by including Afghanistan and Pakistan, which of course are outside the traditional “Middle East.” Other Muslim countries, such as Indonesia (2,139) and Somalia (5,190), do not significantly add to the total.

“Clinton’s State Department was in charge of admissions and the admissions process for people applying to enter from overseas.”

This is a strange and false claim. The vetting of immigrants is done by Homeland Security, specifically its arm known as U.S. Citizenship and Immigration Services. Only after USCIS approves a petition for an immigrant visa does State’s National Visa Center get involved to complete the paperwork for final processing.

“Having learned nothing from these attacks, she now plans to massively increase admissions without a screening plan including a 500 percent increase in Syrian refugees coming into our country.”

President Obama has proposed accepting 10,000 refugees in fiscal year 2016, and in September Clinton said she would like to move toward as many as 65,000. That’s where Trump gets his “500 percent.” (It’s actually 550 percent.) But then he greatly inflates the figure in his next statement. Moreover, Clinton has emphasized there would be careful screening, with an emphasis on those facing religious persecution.

“Under the Clinton plan, you’d be admitting hundreds of thousands of refugees from the Middle East with no system to vet them, or to prevent the radicalization of the children and their children.”

Trump has repeatedly made this “hundreds of thousands” claim, usually referring to Syria, but it’s false. The Obama administration said it would accept a total of 85,000 refugees in 2016 and 100,000 in 2017. That’s from all countries, of which 10,000 would be from Syria in 2016. In fiscal 2013, about 30 percent came from the Middle East, mostly from Iraq. So no matter how you calculate it, it does not add up to “hundreds of thousands.”

Trump also falsely claims there is “no system to vet” refugees. The process actually takes two more years, after vetting that starts with the United Nations High Commissioner for Refugees and then continues with checks by U.S. intelligence and security agencies. (Our colleagues at PolitiFact did a good look at this process.)

“We have to stop the tremendous flow of Syrian refugees into the United States.”

There is no “tremendous flow,” as we have noted. About 1,800 Syrian refugees were admitted to the United States from the beginning of the civil war in Syria to November 2015. The United States is actually well behind on its goal of settling at least 10,000 Syrian refugees this year, with only 2,800 so far in a fiscal year ending Sept. 30.

“Americans already admitted four times more immigrants than any country on Earth, anybody in the world.”

This is a statistic touted by Sen. Jeff Sessions (R-Ala.), a close adviser to Trump. But it’s a dubious one, as it appears based on raw numbers and inconsistent data sets among countries, making it difficult to make an apples-to-apples comparison. The United States is also one of the largest countries in the world in terms of population, so its immigration figures are bound to be among the highest in raw numbers.

A better way to examine this question across large and small countries is net migrants per 1,000 people. On that score, the United States does not rank very high — only 34th in the world in 2015, according to the CIA’s World Factbook.

Trump is correct. As we noted recently in another fact check, since 2000, the last year of the Bill Clinton administration, median household income has been largely flat — $57,576 in January 2000 and $57,243 in April 2016.

“They [Muslims] knew the people in San Bernardino were bad. But you know what? They didn’t turn them in.”

There is no evidence this was the case. There have been unconfirmed second- or third-hand reports — a friend of a friend of a neighbor — that a neighbor claimed to have noticed suspicious activity but did not report anything for fear of doing racial profiling. The religion of this supposed neighbor is unknown, but presumably a fear of racial profiling would suggest the neighbor was not Muslim.

“We’ve spent almost $5 trillion over the years on trying to nation build in the Middle East, and it has been complete and total disaster.”

The wars in Afghanistan and Iraq have cost a lot of money — about $2 trillion in direct costs — but nothing close to $5 trillion has been spent on “nation-building.” The number climbs to between $4 trillion and $6 trillion when future costs for providing medical care and disability benefits for veterans is added, as well as the future cost of servicing the national debt. But Trump suggest the money has already been spent — and specifically for nation-building.

Update: We also did a longer fact check, with a Pinocchio rating, of this Trump statement in the speech: “The immigration laws of the United States give the president powers to suspend entry into the country of any class of persons. Now, any class — it really is determined and to be determined by the president for the interests of the United States. And it’s as he or she deems appropriate.” Follow this link to learn more.